Basic Properties of Fourier Transform

Consider a signal x(t) with Fourier transform X(f). We'll see what happens to the Fourier transform of x(t) on time-reversal and conjugation. i.e:

Now, we are aware that  

Transform X'(f) of x(-t) is: .         Substitute

Therefore, .

Therefore,

Applying this result to periodic signals (we have just seen their Fourier transform), you see that if is the Fourier Series co-efficient of a periodic signal x(t), is the Fourier series co-efficient of x(-t).